Skip to contents

This function constructs a linked (D)GP emulator.


lgp(struc, B = 10, id = NULL)



a list contains L (the number of layers in a systems of computer models) sub-lists, each of which represents a layer and contains (D)GP emulators (represented by instances of S3 class gp or dgp) of computer models. The sub-lists are placed in the list in the same order of the specified computer model system's hierarchy.


the number of imputations to produce the predictions. Increase the value to account for more imputation uncertainties. Decrease the value for lower imputation uncertainties but faster predictions. If the system consists only GP emulators, B is set to 1 automatically. Defaults to 10.


an ID to be assigned to the linked (D)GP emulator. If an ID is not provided (i.e., id = NULL), a UUID (Universally Unique Identifier) will be automatically generated and assigned to the emulator. Default to NULL.


An S3 class named lgp that contains three slots:

  • id: A number or character string assigned through the id argument.

  • constructor_obj: a list of 'python' objects that stores the information of the constructed linked emulator.

  • emulator_obj, a 'python' object that stores the information for predictions from the linked emulator.

  • specs: a list that contains

    1. seed: the random seed generated to produce the imputations. This information is stored for the reproducibility when the linked (D)GP emulator (that was saved by write() with the light option light = TRUE) is loaded back to R by read().

    2. B: the number of imputations used to generate the linked (D)GP emulator.

The returned lgp object can be used by

  • predict() for linked (D)GP predictions.

  • validate() for the OOS validation.

  • plot() for the validation plots.

  • summary() to summarize the constructed linked (D)GP emulator.

  • write() to save the linked (D)GP emulator to a .pkl file.


See further examples and tutorials at


if (FALSE) {

# load the package and the Python env

# model 1
f1 <- function(x) {
# model 2
f2 <- function(x) {
  2/3*sin(2*(2*x - 1))+4/3*exp(-30*(2*(2*x-1))^2)-1/3
# linked model
f12 <- function(x) {

# training data for Model 1
X1 <- seq(0, 1, length = 9)
Y1 <- sapply(X1, f1)
# training data for Model 2
X2 <- seq(0, 1, length = 13)
Y2 <- sapply(X2, f2)

# emulation of model 1
m1 <- gp(X1, Y1, name = "matern2.5", linked_idx = c(1))
# emulation of model 2
m2 <- dgp(X2, Y2, depth = 2, name = "matern2.5")
# assign linking information after the emulation construction
m2 <- set_linked_idx(m2, c(1))

# emulation of the linked model
struc <- combine(list(m1), list(m2))
m_link <- lgp(struc)

# summarizing

# prediction
test_x <- seq(0, 1, length = 300)
m_link <- predict(m_link, x = test_x)

# OOS validation
validate_x <- sample(test_x, 20)
validate_y <- sapply(validate_x, f12)
plot(m_link, validate_x, validate_y, style = 2)

# write and read the constructed linked emulator
write(m_link, 'linked_emulator')
m_link <- read('linked_emulator')